Heat olive oil in a large, deep skillet or straight-sided sauté pan over high heat until shimmering. Add chopped onions, stirring frequently until they start to caramelize. (About 5 minutes)
Add Aleppo pepper, cumin, turmeric and cayenne pepper and stir for a minute to release flavors.
Add diced tomatoes and paste and stir to combine. Reduce heat to a simmer and cook for 10 minutes, then season to taste with salt and pepper.
Break an egg in a small bowl. Using a large wooden spoon, make and hold a well in the sauce near the perimeter of the pan. With the other hand gently slide the egg into it. Spoon a little sauce over edges of egg white to partially submerge and contain it, leaving yolk exposed.
Repeat with remaining 3 eggs, working around pan as you go.
Season eggs with a little salt, reduce heat to a quick simmer and cook uncovered until egg whites are barely set and yolks are still runny, 8 to 10 minutes. Spread the whites occasionally to cook through. ( If you prefer the yolks less runny, cook with the pan covered.)
Sprinkle with cilantro or parsley and a drizzle of olive oil. Serve immediately with crusty bread.